Former Bayern Munich and Crystal Palace defender Ismael was appointed as Gerhard Struber's successor on Friday and is tasked with igniting the Tykes' season.
The 45-year-old Frenchman was given a watching brief at The Den and witnessed a battling performance from his new side.
Murray said: "I don't know a great deal about him, but obviously we know coming into the club that he'll fit our philosophy.
"I'm excited to work with him – for me as a young English coach, it's someone from another culture that I can hopefully take bits on and he can hopefully make us better and help us stay in the Championship."
On his side's third draw on the spin, Murray added: "I thought, for us, it was a real good away performance.
"I think when you come to a place like this, with a team that's in the play-off places before the game, there are times where you're going to be stressed out but I thought our game plan worked well.
"I think we caught them a few times on the counter-attack, but again our final pass needs to be a little bit better for us to take the opportunities that we do have.
"As you expect, at certain points in the game you're going to be under the cosh and we relied on Jack [Walton] a couple of times to get us out of trouble."
Following 44 minutes of tedium, Mowatt fired Barnsley into the lead with a fantastic strike into the top corner from 25 yards after a defensive header had fallen his way.
Millwall were level right on the stroke of half-time, however, when Cooper struck with a header from Connor Mahoney's corner.
Barrett said: "Obviously, it's not ideal.
"Your manager goes down with Covid, so it's been an unusual 24 hours, but the good thing with modern technology now is you can keep in contact and the gaffer was still able to do his meeting by video.
"Firstly, he's feeling okay, so we wish him a speedy recovery and hopefully he's back in the dugout soon.
"It's not ideal but we've got to get on with it and we've got some great staff here and people who all pull together and work together.
"The second half was frustrating because I thought we'd done enough to win the game.
"I thought we were disappointing in the first half – we played into their hands.
"They were very aggressive on the press and I thought we turned the ball over too cheaply, so we were disappointed with that, but the second half was a much better performance."